Question

find two rational numbers between 1/2 and 1/3

Answer 1

5/4 and 19/12 are the answers

Answer 2

Answer:

7/18 and 8/18 or 4/9

Step-by-step explanation:

$\text{To find 2 rational numbers between \dfrac{1}{2} and \dfrac{1}{3} , first, take the LCM of their denominators}\\\\\\\text{and, write their equivalent fractions having the same denominator.}\\\\\text{LCM of 2 and 3 is 6.}\\\\\dfrac{1}{2} = \dfrac{1 \times 3}{2 \times 3} = \dfrac{3}{6}\\\\\\\dfrac{1}{3} = \dfrac{1 \times 2}{3 \times 2} = \dfrac{2}{3}\\\\\\\text{Now, the next step is to multiply the fractions by \dfrac{n+1}{n+1} , where n is the no. of rational}$

$\text{numbers to be found. So, in case, we have to find 2 rational numbers, so we will}\\\text{multiply the fractions by}}\\\\\dfrac{2+1}{2+1} = \dfrac{3}{3}\\\\\\\text{Now,}\\\\\dfrac{3 \times 3}{6 \times 3} = \dfrac{9}{18}\\\\\\\text{And,}\\\\\dfrac{2 \times 3}{6 \times 3} = \dfrac{6}{18}\\\\\\\text{Clearly, 2 rational numbers between \dfrac{1}{2} and \dfrac{1}{3} or \dfrac{9}{18} and \dfrac{6}{18} are:}$

$\large \boxed{\boxed{\bold{\dfrac{7}{18}, \: and \: \dfrac{8}{18}, \: or \: \dfrac{4}{9}.}}}$

Hope it helps !! Do comment if you have any doubts.